Riemann-Roch for equivariant Chow groups

Details Riemann-Roch for equivariant Chow groups Riemann-Roch for equivariant Chow groups

1999-05-13

arxiv.org/abs/math/9905081v2

Mathematics

Algebraic Geometry

31 pages, Latex2e. Email for W. Graham is wag@math.uga.edu Duke Math. Journal, to appear

Scientific paper

The purpose of this paper is to prove an equivariant Riemann-Roch theorem for schemes or algebraic spaces with an action of a linear algebraic group $G$. For a $G$-space $X$, this theorem gives an isomorphism between a completion of the equivariant Grothendieck group and a completion of equivariant equivariant Chow groups. The key to proving this isomorphism is a geometric description of completions of the equivariant Grothendieck group. Besides Riemann-Roch, this result has some purely $K$-theoretic applications. In particular, we prove a conjecture of K\"ock (in the case of regular schemes) and extend to arbitrary characteristic a result of Segal on representation rings.

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